Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

55.1K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
55.1K
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

639
Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
639
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

7.6K
Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
7.6K
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

12.2K
Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
12.2K
Fermi Level Dynamics01:12

Fermi Level Dynamics

492
The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
492
The de Broglie Wavelength02:32

The de Broglie Wavelength

32.0K
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
32.0K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Advancing In-Context Learning for Efficient and Stable Medical Report Generation.

IEEE transactions on pattern analysis and machine intelligence·2026
Same author

Assembled Melamine-Regulated Synthesis of Uniform Manganese Dioxide Nanoribbons for Superior Heating Effect.

ACS applied materials & interfaces·2025
Same author

Prefrontal activity to negative emotions moderates the longitudinal links between parents and youth's internalizing symptoms.

Cerebral cortex (New York, N.Y. : 1991)·2025
Same author

Mothers Under Pressure: Different Types of Pressure and Chinese Mothers' Quality of Homework Involvement in Daily Life.

Family process·2025
Same author

Scrutinizing parental minimization reactions to adolescents' negative emotions through the lens of Chinese culture.

Journal of research on adolescence : the official journal of the Society for Research on Adolescence·2024
Same author

Chinese Mothers' Reactions to Adolescents' Positive Emotions: Relations to Adolescents' Emotional Adjustment and Mothers' Socialization Goals.

Journal of youth and adolescence·2023

Related Experiment Video

Updated: Nov 27, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.8K

Quantum Weak Invariants: Dynamical Evolution of Fluctuations and Correlations.

Zeyi Shi1, Sumiyoshi Abe1,2,3,4

  • 1Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary

Weak invariants in open quantum systems exhibit growing fluctuations over time, unlike conserved quantities. This temporal asymmetry differs from entropy measures and is described by a new formula for their covariance matrix.

Keywords:
Gorini–Kossakowski–Lindblad–Sudarshan equationcompletely positive mapscovariance matrixmonotonic growth of fluctuations of weak invariantsvon Neumann and Rényi entropies

More Related Videos

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.8K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.4K

Related Experiment Videos

Last Updated: Nov 27, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

8.8K
Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

14.8K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.4K

Area of Science:

  • Quantum mechanics
  • Open quantum systems
  • Quantum information theory

Background:

  • Weak invariants are time-dependent observables with conserved expectation values in quantum systems.
  • Their fluctuations, however, are not constant over time, indicating a departure from simple conservation laws.
  • Understanding the dynamics of these fluctuations is crucial for characterizing open quantum systems.

Purpose of the Study:

  • To investigate the temporal evolution of fluctuations of weak invariants in open quantum systems.
  • To compare the behavior of weak invariants with established entropy measures (von Neumann and Rényi entropy).
  • To develop a theoretical framework for describing the time evolution of weak invariants under general quantum dynamics.

Main Methods:

  • Assuming time evolution governed by a completely positive map.
  • Analyzing the behavior of fluctuations even when the map is not unital.
  • Deriving a formula for the covariance matrix evolution under the Gorini-Kossakowski-Lindblad-Sudarshan equation.

Main Results:

  • Fluctuations of weak invariants monotonically grow over time, irrespective of whether the quantum map is unital.
  • This monotonic growth of fluctuations provides a distinct signature of temporal asymmetry compared to entropy measures.
  • A formula for the covariance matrix evolution of weak invariants was derived for systems described by the Gorini-Kossakowski-Lindblad-Sudarshan equation.

Conclusions:

  • Weak invariants offer a novel perspective on temporal asymmetry in open quantum systems, distinct from entropy-based approaches.
  • The monotonic growth of their fluctuations, even under non-unital maps, highlights their unique dynamical properties.
  • The presented formula facilitates the study of weak invariant dynamics in realistic open quantum systems governed by master equations.